Could RCTs be used in macro policy?

Clearly, the nations of the world are not going to line up to let me randomize their monetary policy. But what if I could convince one to do so? 

Randomized control trials (RCTs), when ethical and possible, present the most reliable way to measure the impact of policy. Units of randomization, for instance people, are put into a treatment group, who gets a program or policy, and a control group, that doesn't get the program or policy. You compare outcomes for the two groups to see the impact of the program.

The key to the validity of the RCT is that the sample size has to be big enough that when you randomly divide into treatment and control, there are no important systemic differences between the two groups. Randomization isn't used to evaluate macroeconomic policies for 2 reasons: 1) it is usually too important for people to allow it to be randomized, and 2) it has to be enacted at a high level-- national or maybe state or province-- so it is difficult to get a large enough sample.

But what if we randomized, not by entities like people or countries, but across years? For example, what if the Federal Reserve allowed me to randomly change the policy interest rate by +25 basis points, 0 basis points, or -25 basis points? Over a long enough time frame, the periods that fall into each randomization group should be statistically the same on average. This would allow us to look at the effect of the interest rate change on the economy. 

Of course, there are some kinks to be worked out. Similar to spillover effects, policy changes have impacts across multiple periods; however, these could be measured and accounted for. Another problem is checking the balance of the randomization. There would be no equivalent to a baseline, and you couldn't stratify, since you don't know the attributes of future time periods in advance. These problems would imply that you need a very large sample size. 

There are certainly other methodological challenges I haven't thought of. I imagine I will have plenty of time to think through them before the first problem-- the fact that politicians, who insist they can control things they can't, would never randomize something they can-- is solved. But if anyone hears about a central bank looking for a monetary policy consultant, let me know.